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Harshad n.  and  taxicab n.

First numbers that belong to both sets:

1729, 4104, 32832, 39312, 46683, 110656, 110808, 134379, 165464, 171288, 262656, 314496, 373464, 402597, 513000, 513856, 525824, 558441, 842751, 886464, 920673, 1009736, 1016496, 1061424, 1075032, 1080891, 1331064, 1370304, 1407672, 1533357, 1728216, 1729000, 1734264, 1774656, 2101248, 2515968, 2562112, 2864288, 2987712, 2991816, 3220776, 3375008, 3512808, 3551112, 3628233, 4104000, 4123000, 4174281, 4467528, 4511808, 4607064, 4624776, 4673088, 4914000, 5462424, 6013000, 6017193, 6517000, 6742008, 7091712, 7094269, 7365384, 7872536, 8131968, 8275176, 8491392, 8600256, 8647128, 9016488, 10036845, 10083528, 10424232, 10870119, 10962432, 11261376, 11478584, 11985003, 12266856, 12650337, 12874176, 13484016, 13489875, 13825728, 13851000, 13874112, 13915125, 14197248, 14482503, 15187041, 15201368, 15682680, 16012269, 16387128, 16797375, 18410392, 19250163, 20127744, 20162952, 21411000, 21753576, 21994875, 22544704, 23901696, 23934528, 25164405, 25371171, 25766208, 25785432, 27000064, 27003375, 27262872, 27445392, 27882127, 28102464, 28149336, 29025864, 29503656, 30511936, 32268024, 32530680, 32832000, 33108264, 33394248, 34031907, 35740224, 36047592, 36094464, 36856512, 37384704, 37498032, 38007144, 39312000, 40033000, 40354119, 41080832, 41258737, 41400639, 41892515, 42154840, 42301656, 43450344, 43570872, 43777216, 43852536, 43997625, 46394712, 46661832, 46683000, 46825128, 47915712, 48137544, 50324625, 51479064, 51564032, 52324272, 53936064, 54267003, 54887625, 58923072, 61568208, 62135073, 63057960, 64125000, 64623104, 65055744, 66201408, 67173463, 67931136, 67944312, 68802048, 69177024, 71292312, 71509312, 72131904, 74093832, 74130875, 80102574, 80208576, 80294760, 80668224, 80779032, 84266000, 85502375, 87699456, 90091008, 91034307, 91125027, 91125216, 92384712, 92456000, 94820544, 95880024, 100092456, 100711000, 101194704, 101202696, 101700872, 102025280, 102562551, 102993408, 107872128, 107919000, 110087432, 110605824, 110656000, 110808000, 111321000, 111906333, 114103808, 115084125, 115860024, 115942104, 117132750, 118974960, 120623256, 121496328, 121610944, 121660623, 121818816, 122262264, 123262120, 124336000, 124390728, 125461440, 126173376, 126217000, 126906624, 127062000, 128098152, 131997229, 132678000, 134379000, 135111375, 136004184, 136364536, 136591000, 141117704, 147748104, 150611643, 151212412, 152275032, 154001304, 154245637, 154573272, 155722203, 159220431, 161021952, 161303616, 161801432, 162259704, 162351000, 162464211, 165464000, 168223608, 168293944, 169003072, 171288000, 171904005, 174028608, 175959000, 176252608, 176427433, 182034216, 191213568, 191476224, 191669625, 198156016, 198865368, 201159000, 201315240, 203415121, 205556904, 206129664, 206283456, 207500608, 212051736, 212314473, 212558472, 212820615, 214852608.

Some larger examples :